NMR Spectroscopy Theory
-
Atomic nuclei have a “spin” associated with them (i.e., they act as if
they were spinning about an axis) due to the spin associated with their
protons and neutrons.
-
Because nuclei are positively charged, their spin induces a magnetic
field. When a magnetic field is applied to atomic nuclei, the magnetic
fields of the nuclei align themselves either parallel or antiparallel to the
applied magnetic field.
-
The nuclei have a slight preference for the parallel alignment, as it
has a slightly lower energy, but nuclei can flip between the two possible
alignments.
-
When EM radiation with energy equal to the energy difference between
the two alignments is applied to the nuclei, it induces them to flip from
parallel to antiparallel alignment. Rapid flipping between alignments
occurs. The nuclei are said to be in resonance, and the energy they emit
when flipping from the high to the low energy state can be
measured.
-
The energy at which a given nucleus achieves resonance depends on its
chemical surroundings.
-
NMR spectra are taken by applying a magnetic field to as ample,
irradiating the sample with EM radiation whose energy is varied over a given
range, and measuring the energy emitted by flipping nuclei at each energy.
-
The range of radiation energies is generally chosen such
that emission from only one type of nucleus (e.g., 1H) in a
molecule is seen.
-
NMR spectroscopy does not work for nuclei that have an
even number of protons and neutrons—these nuclei have no net
spin.
-
NMR spectroscopy is most commonly done on 1H and
13C.
Features of an NMR Spectrum
-
NMR spectra are displayed as plots of intensity of energy emission
(due to resonance) versus the energy of the radiation applied to the sample.
Peaks in the spectrum represent resonance energies for nuclei in a
molecule.
-
Shielding: An electron cloud circulates
around each nucleus and creates a small magnetic field opposing the applied
magnetic field. The electron cloud around each atom depends on the
surrounding atoms. As a result, each nucleus experiences a slightly
different magnetic field (the sum of the applied field and the field from
the electron cloud). For this reason, the energy at which a nucleus achieves
resonance depends on its surroundings.
-
Chemical shift (δ): The resonance energy for
a given nucleus is reported in an NMR spectrum as the difference (in
parts/million) between the resonance frequency for a given proton and the
resonance frequency for protons in a reference compound, which is usually
tetramethylsilane, (CH3)4Si. Chemical shifts give information about the
atomic surroundings of a given nucleus.
-
Peak intensity: The area under a peak in an
NMR spectrum is proportional to the number of nuclei in a given chemical
environment in a molecule (e.g., if the area under a peak is two times the
area under another peak, there are twice as many nuclei responsible for the
larger peak than for the smaller one).
-
The intensity of an NMR peak gives information about the
relative number of a given type of nucleus in a
molecule.
-
Spin-spin splitting: In 1H NMR, a given
hydrogen nucleus interacts with hydrogen nuclei on neighboring carbon atoms
such that the peak from that nucleus is split into multiple peaks called a
multiplet. If a hydrogen nucleus has an hydrogen nuclei on adjacent atoms,
its NMR signal is split into (n + 1) separate peaks. Relative intensities of
the peaks in a multiplet follow Pascal’s triangle.
-
Spin-spin splitting gives information about the hydrogen
atoms neighboring a given hydrogen nucleus.
How To Interpret An NMR Spectrum
This handout relates the basic theory of NMR
described on the theory web handout
with spectra of real molecules and how to deduce structure from the spectra.
Before reading this handout, you need to be thoroughly familiar with all
of theory concepts that were described.
1.0 The
NMR spectrum.
1.1 Because different amounts of electron density are around
different non-eqivalent nuclei, the different non-equivalent nuclei
in a molecule are experiencing slightly different net magnetic fields
in an NMR experiment
(Review Section 5.2A
of the theory handout). Recall also that the difference in energy
between the two allowed spin states (+1/2 and -1/2 spin states) of
a spin 1/2 nucleus (like in 1H and 13C nuclei) depends on the exact
magnetic field felt by the nucleus
(Review
Section 2.3C in the theory handout). Recall further that
in the NMR experiment, when and only when nuclei are irradiated with
electromagnetic radiation of energy that
exactly corresponds
to the energy difference between the +1/2 and -1/2 spin states, the
nuclei absorb the energy and the NMR spectrometer measures this absorbance
(Review section 3.1 of the theory
handout). The absorbance of energy to convert a nucleus from a
+1/2 to a -1/2 spin state is referred to as "resonance"
of that nucleus.
1.1A
The key conclusion is that nuclei with different electron densities
have +1/2 and -1/2 spin states that differ in energy by differing
amounts, so these nuclei will absorb electromagnetic radiation of
different frequencies in the NMR experiment.
1.1B Nuclei
surrounded by greater amounts of electron density will be more shielded
from the external magnetic field, so they will absorb electromagnetic
radiation of lower energy, that is, lower frequency (energy
is proportional to frequency). You may want to review
Section 5.2A of the theory handout
again.
1.1C
The converse is also true, namely that nuclei surrounded by lesser
amounts of electron density will be less shielded (referred to as
being "deshielded") from the external magnetic field,
so they will absorb electromagnetic radiation of higher energy,
that is, higher frequency (energy is proportional to frequency).
1.1D The
three most important factors influencing the electron density
around a hydrogen nucleus are: (i) adjacent electronegative atoms
remove electron density; (ii) hybridization of the attached carbon
atom, increasing shielding is observed in the order sp2,
sp, sp3; (iii) adjacent pi bonds are deshielding, which relates
to (ii).
1.2
An NMR spectrum is a plot of absorbance versus frequency.
1.2A To make
different spectra directly comparable, a standard is used for all
NMR spectra. For 1H NMR spectra, the standard is called tetramethylsilane
(TMS) and a small amount of TMS is usually added to any 1H
NMR sample.
1.2B Magnets of different strengths lead to absorbance
of electromagnetic radiation at different frequencies for the
same nucleus, meaning that if simple frequency were plotted in
an NMR spectra, you could not compare spectra taken of the same
sample on machines with different magnet strengths. To solve this
problem,
the frequency of absorption plotted on NMR spectra are corrected
for the magnet strength. In addition, frequency is correlated
to the reference compound TMS. The
frequency at which TMS absorbs is defined as 0 frequency by convention.
In the NMR spectrum, absorbance frequencies of electromagnetic
radiation are plotted as chemical shift (d)
listed in units called parts per million
(ppm) that is defined by the following equation:2.0 The nuclear
spin of hydrogen atoms creates a magnetic field that influences the chemical
shift of nearby hydrogen atoms (Review Sections
5.1 and 5.2).
2.1 Nuclear spin magnetic fields will influence
hydrogen atoms that are three or fewer bonds away from each other in the
same molecule. Hydrogen atoms that are four or greater
bonds away usually do not influence each other.
2.2 A hydrogen atom with a nuclecus in a
spin state of +1/2 produces a slightly different magnetic field than
a one in a –1/2 spin state.
2.3 Even in a strong magnetic field, across
a population of molecules, there is only a very slight excess of nuclei
in the +1/2 spin state.
2.4 Putting all of these ideas together means
the following: Consider a hydrogen X adjacent (three bonds away) to another
hydrogen Y in a molecule. In around half of the molecules in the NMR sample,
hydrogen X feels the magnetic field from a Y with nuclear spin of +1/2.
The other half feel from Y a nuclear spin of –1/2. Thus, when you look
at the spectrum, there are actually two different, but closely spaced peaks
as the signal for hydrogen X. This phenomenon is called “spin-spin”
splitting, and the distance between the two signals for X is called the
“coupling constant”, often denoted as “J”. Similarly,
the signal for Y actually has two peaks because of spin-spin splitting by
X.
2.5 Consider a –CH2-
group adjacent to a hydrogen X. Both of the hydrogen
atoms in the –CH2- are chemically equivalent
and could be either in the +1/2 or –1/2 nuclear spin state. Thus, there
are three situations possible: i) +1/2,+1/2; ii) +1/2,-1/2,
which is the same as –1/2, +1/2 and iii) –1/2,-1/2. Thus,
there are actually three different magnetic fields that are felt by X in
molecules of the sample, in a 1:2:1 ratio. Thus, the signal for hydrogen
X is split into three peaks in a 1:2:1 ratio.
2.6 The same holds for a –CH3
group, that will split an adjacent hydrogen signal into four peaks, with
a 1:3:3:1 ratio. You should verify this for yourself by making all the possible
combinations of nuclear spins for the three equivalent hydrogen atoms of
a methyl group.
2.7 In the general case, N equivalent hydrogen
atoms will split an adjacent signal into (N+1) peaks, with relative
ratios that are predicted by Pascal’s triangle (Figure 13.16 in
the book).
3.0 Following the
same logic, the splitting should multiply if a single hydrogen atom
is adjacent to hydrogen atoms on either side. Think about combining
all the possible nuclear spin states for these nearby sets of hydrogen atoms.
Thus, if you have a hydrogen atom X between one –CH
2-
and one –CH
3 group, it should be split into an
amazing (2+1) x (3 + 1) = 12 signals because there are that many different
combinations of +1/2 and -1/2 spins possible.
3.1 Thus, if
the coupling constants (J) from the –CH2- and
–CH3 groups are significantly different from
each other, then 12 peaks will be observed as the signal for hydrogen X.
3.2 However,
in practice, coupling constants (J) are pretty close to the same value for
almost all sets of hydrogen atoms in organic molecules, simplifying the
splitting pattern, since now many of the twelve peaks will overlap with
each other. What this means is that for almost all the spectra you will
see, if a hydrogen X is surrounded by N hydrogen atoms, the signal for X
will be split into only (N+1) peaks, no matter how those N hydrogen atoms
are grouped in terms of sets of equivalent atoms. Thus, what is actually
seen for the example above is that the signal for X would appear
in the spectrum to be split into 2 + 3 + 1 = 6 peaks, not 12, peaks. This
is the so-called “N+1” rule.
3.3 The diagram below shows these two different situations. When
nuclei from hydrogen atoms Z and Y split the signal for hydrogen X with
very different coupling constants (notice how the coupling constant J for
the red Z hydrogen nuclei is larger than J for the blue Y hydrogen nuclei),
all twelve peaks are spread out and identifiable. Below that is shown the
situation in which the coupling constants are the same for nuclei of both
Z and Y, so only 6 peaks are actually observed in the signal for hydrogen
X due to extensive overlap. This latter case, with six peaks, is what you
will almost always see in reality since coupling constants tend to be similar
in organic molecules.
3.3 The above explanation of splitting can confuse students for
a while. The important point is that in the example given, you
see 6 different peaks in the spectrum (N+1 rule) even though there are really
12 peaks produced, it is just that several of them are on top of each other
because the coupling constants are the same. For alkyl groups in organic
molecules, the coupling constants are generally the same so you will almost
always see the fewer peaks, corresponding to the simple N+1 rule, rather
than the greater number of peaks derived from the multiplication rule.
3.4 The bottom
line here is that by seeing how a given signal is split, you can figure
out how many hydrogen atoms are adjacent on the molecule, namely the number
of peaks in the signal minus 1. From this information you can piece together
what a molecule looks like if you know how many atoms of each
type are present (i.e. the molecular formula such as C4H10N2O).
You get the molecular formula information from something called a mass spectrum,
described later in the text. Molecular formulas will be provided to you
in homework or test questions.
4.0 For a given
signal, integrating the signal (include all splitting peaks for a given signal)
gives you a relative value that is proportional to the number of equivalent
hydrogen atoms that gave rise to the signal. Thus, by looking at the integration
values, you can deduce how many of each type of equivalent hydrogen atoms
are in the molecule. For example, a -CH3 group would
have a signal that integrates to a relative value of 3 (no matter how the
signal is split), and a -CH2- group would have a relative
integration of 2, etc. Note that sometimes integrations are simply given as
absolute numbers, and you must find the common factor to deduce how many hydrogen
atoms are represented by each integration value.
5.0 Putting it all together: How to deduce a structure
from an NMR spectrum. First, you must be given the molecular formula, so you
know how many of each type of atom are present. Second, count the number of
different signals and their relative integrations to see how many different
sets of equivalent hydrogen atoms are in a molecule, and how many of each
set are present. Compare the chemical shifts of each signal to tables to identify
what functional groups are present. Finally, use the signal splittings to
determine which hydrogen atoms must be no more than 3 bonds away from each
other.
6.0 For alkenes,
the pi bond prevents bond rotation so the different hydrogen atoms on an unsymmetrical
alkene are not equivalent, so they all have different signals, and splitting
follows the multiplicative rule (the coupling constants are usually significantly
different for geminal vs. cis. vs. trans relationships).
7.0 For hydrogens
in a -CH2- group adjacent to a chiral center, the
two different H atoms are no longer equivalent, because even with bond
rotation, the two hydrogens are never in the same environment with respect
to the groups on the adjacent chiral center. Thus, each H of -CH2-
group adjacent to a chiral center usually has its own signal in the NMR
spectrum.
//////////
Irbid, known in ancient times as Arabella or Arbela, is the capital and largest city of the Irbid Governorate.
Wikipedia
/////////////